Question

The sum of a number and its reciprocal is 10/3. Finds the number

Answer 1

Let the number be a

According to question,

a + 1/a = 10/3

=> (a^2 +1) /a = 10/3

=> 3a^2 +3 = 10a

=> 3a^2 - 10a +3 = 0

=> 3a^2 - 9a - a +3 = 0

=> 3a ( a - 3) - 1(a - 3) = 0

=> (3a - 1) (a - 3) = 0

a = 3 and 1/3

If number = 3, reciprocal = 1/3

If number = 1/3 reciprocal = 3

Answer 2

Let the no. be x  Hence reciprocal = 1/x Now given that :                     x + 1/x = 10/3                 Equating the denominator                  3(x^2 + 1) = 10x                   3x^2 - 10x + 3 = 0                   3x^2 - 9x - x + 3 = 0                   3x(x - 3) -1(x - 3) = 0                   (3x - 1)(x - 3) = 0                                 Hence, x = 1/3 or x = 3